But if you want to learn scripting today on Windows, go for Powershell.
Here is a script that removes the .BluRay for all .mkv files in alla sub directories, just like the other one, create a file with .bat extension in the directory and run it.
I forgot to say it an my first post, but you should always try on just one or two files that you've copied to a directory for testing.
for /f "tokens=*" %%m in ('dir /s /b *.BluRay.mkv') do (
ren "%%m" "!nn!.mkv"